The fairy tale context always made Baby Bear's existence (as well as his family, for that matter) within the Sesame universe a little . . . unconventional for me to believe? I can't really think of any other way to put it, but I mean, all of the other Muppet characters are original to their universe, but Baby Bear is an already-existing character (and I suppose fairy tale characters are public domain).
Then again, I supposed it's not entirely unbelievable, considering the street has played host to a number of spastic fairy tale characters over the years - but somehow, Baby Bear was the only one who seemed to work as part of the regular Muppet family.